Role Privilege Inheritance

Problem Statement

You are given a role table in a company organization where every employee has a role. The role table consists of a unique string role and a unique string privilege. The company has a hierarchical structure, meaning each role inherits the privileges of its parent role, and each role can have only one parent.

Write an API:

• void init(PrivilegeRoles privileges): Initializes the system with a list of roles and the privileges they inherit from.
• List<String> roleInheritance(String role): Returns a list of roles that directly or indirectly inherit the privileges of the given role. The returned list should exclude the given role itself.

Constraints

1. 1 <= privileges.length <= 10^5
2. 1 <= privileges[i].parent.length <= 10
3. 1 <= privileges[i].child.length <= 10
4. privileges[i].parent != privileges[i].child
5. parent and child consist of lowercase English letters.
6. There are no circular dependencies between roles.
7. For roleInheritance, the given role must exist in the system.

Examples

Example 1:

Input: privileges = [ ["role1", "role2"], ["role2", "role3"], ["role3", "role3"], ["role3", "role4"] ] role = "role2"

Output: ["role3", "role4"]

Explanation:

role2` has the direct privilege of `role2`, and indirectly inherits `role3` and `role4`.
`

### Example 2:

**Input:**
`
privileges = [
    ["role1", "role2"],
    ["role2", "role3"],
    ["role2", "role4"]
]
role = "role1"
`

**Output:**
`
["role2", "role3", "role4"]
`

**Explanation:**
`
role1` has the direct privilege of `role1`, and indirectly inherits `role2`, `role3`, and `role4`.

Hints

1. Use a graph-based approach to model the hierarchical structure of roles.
2. Perform a depth-first search (DFS) or breadth-first search (BFS) to find all roles that inherit the privileges of the given role.